Is it possible to create a page (like igoogle) where user should be able to drag and drop the portlets to a different column or rows (user should not logged in)

The main point of your question probably is "user should not logged in". By default, liferay requires users to be logged in to add portlets and to manage pages. If you want to allow non-logged in users to add portlets and to manage pages, you have to give permission to the "guest" user. Unfortunately, all users not logged in will have the same page.

I don't want user to add protlets. wanted give a flexibility to guest user to move available portlets on the page.Please find the attached image.Referring to attached image - Guest user should be able to move available portlets on the page - ExampleMessage Boards can be moved below My GreetingDocument Library can be moved to Message Boards etc